In New York, there are lots of rental brokers, but they're expensive (typically they charge 15% of a year's rent for their services).
On the off chance that you are talking about NY, streeteasy.com, urbansherpany.com, and nybits.com are good places to search for listings/do research on buildings and price ranges and such.
Padmapper.com or a realtor. At least with the realtor my friend used in finding her apartment, she was not charged. The person trying to rent out the apartment paid for the realtor.
We used a realtor when we were relocated across country. We only had a weekend to find a place to rent, so it was much simpler to let someone else do the legwork.
Check out the local online news channels/newspapers. We have a local channel that has a great board for rentals, housing and the like. It might be worth the look.
Padmapper.com or a realtor. At least with the realtor my friend used in finding her apartment, she was not charged. The person trying to rent out the apartment paid for the realtor.
Love padmapper. And highly recommend a relocation/rental specialist/realtor in the area.
There are apartment finder offices all over here in San Antonio. I don't know where you are moving to, but if that type service is available, do it. The apartment complexes pay them to place you. We had a great experience when we had not much time to search, very helpful.